variables not being saved?

I just included the code for U here, but neither L nor U are being saved, but they can both be displayed? I'm trying to use the values for L and U as inputs in another function, but it says "unrecognized variable"

function [L,U] = lumine(A)
%lumine: LU decomposition
%input:
%A = coefficient matrix
%output:
%L = lower matrix
%U = upper matrix
[m,n] = size(A); % defines m and n
if m~=n  %checks to see if the matrix is square
    error('Matrix A must be square') % displays error if matrix is not square
end 
if det(A) == 0 %checks to see if the matrix is singular
    error('Matrix cannot be singular')
end
% forward elimination
Afake = A;
for k = 1:n % starts at position 1, goes to the last column
    for i = k+1:n %starts at the row after k, goes to the second to last row
        factor = Afake(i,k)/Afake(k,k); %defines factor as the element directly below one of the elements in the diagonal, divided by that element on the diagonal
        Afake(i,1:n) = Afake(i,1:n)-factor*Afake(k,1:n); %for each row of the matrix, the row before is multiplied by factor, which is then subtracted
        
    end
end
U = Afake; % A becomes the upper matrix after every row is completed 
End 

[Walter Roberson]

You never assign anything to L

[Olivia]

I do, I just didn't show the code for it because it's the same as U.

[Olivia]

for k = 1:n % starts at the first element, goes until the last
    for i = k+1:n % starts at the element after k, goes until the second to last
        factor = A(i,k)/A(k,k); %defines factor as the element directly below one of the elements in the diagonal, divided by that element on the diagonal
        A(i,k) = factor; % stores the factor for that iteration in the element A(i,k)   
    end
    A(k,k+1:n) = 0; % makes every element after the diagonal = 0
    A(k,k) = 1; %makes every element on the diagonal = 1
end
A(3,2) = 1.5;
L = A; % A becomes the lower matrix

[dpb]

You forgot to show us where/hos you tried to use the results and got the error...

Include the error text and context in its entirety...

[Olivia]

q = [2 1 -1; 4 0 2;8 1 0];
lumine(q)
B = [-1;-2;-3];
lusolver(L,U,B)

Unrecognized function or variable 'L'.

Error in untitled40 (line 5)
lusolver(L,U,B)

[dpb]

You didn't save the results you calculated to be used in the next piece of the code...see Answer for revised code.

Read the function documentation and especially the <section on workspaces>. The scope of function variables is local to the function.

[Umar]

Hi @Olivia,

I have updated both functions. The updated provided code consists of two functions: lumine and lusolver.The lumine function performs the LU decomposition of a given coefficient matrix A and returns the lower matrix L and upper matrix U. It follows the following steps:Checks if the matrix A is square. If not, it throws an error and also if the matrix A is singular. If yes, it throws an error.Then, it initializes L as an identity matrix and U as A.Performs the LU decomposition using nested loops.Updates the rows of U and store the factors in L and sets the diagonal elements of L to 1.The lusolver function takes the lower matrix L, upper matrix U, and a vector B as inputs and solves the system of linear equations using LU decomposition. It follows the following steps:Initializes vectors y and x with zeros., performs forward substitution to solve Ly = B and backward substitution to solve Ux = y. Afterwards, returns the solution vector x.

Lumine Function

    function [L,U] = lumine(A)

    % lumine: LU decomposition

    % input:

    % A = coefficient matrix

    % output:

    % L = lower matrix

    % U = upper matrix

    [m,n] = size(A); % defines m and n

    if m ~= n  % checks if the matrix is square

        error('Matrix A must be square');

    end 

    if det(A) == 0 % checks if the matrix is singular

        error('Matrix cannot be singular');

    end

    % Initialize L as an identity matrix and U as A

    L = eye(n); 

    U = A;

    for k = 1:n % starts at position 1, goes to the last column
        for i = k+1:n % starts at row after k, 
         goes to second to last row

            factor = U(i,k)/U(k,k); % defines factor

            U(i,k:n) = U(i,k:n) - factor * U(k,k:n); 
            % update row i of U

            L(i,k) = factor; % store factor in L

        end

     end

    % The diagonal of L should be set to 1 (identity property)
    for i = 1:n

        L(i,i) = 1; 

     end

     end

     q = [2 1 -1; 4 0 2; 8 1 0];

     [L,U] = lumine(q); 
     % Now both L and U will be defined correctly.

     disp('Matrix L:');

     disp(L); % Display the lower matrix L

     disp('Matrix U:');

     disp(U); % Display the upper matrix U

Lusolver function

    function solution = lusolver(L, U, B)

    n = length(B);

    y = zeros(n, 1);

    x = zeros(n, 1);

    % Forward Substitution (Ly = B)

    for i = 1:n

        y(i) = B(i) - L(i,1:i-1)*y(1:i-1);

    end

    % Backward Substitution (Ux = y)

    for i = n:-1:1

        x(i) = (y(i) - U(i,i+1:n)*x(i+1:n)) / U(i,i);

    end

    solution = x;

    end

    B = [-1;-2;-3];

    solution = lusolver(L,U,B);

    disp(solution);

Please see attached.

Hope, after this detailed explanation and provided two updated functions, your problem is resolved. Please let me know if you still have any further questions.

Answer 1

[dpb]

As I suspected, you didn't return the values you calculated when you called lumine; L and U are local variables insidee the function and unless they are stored when the function is called, they're lost....

q = [2 1 -1; 4 0 2;8 1 0];
[L,U]=lumine(q);
B = [-1;-2;-3];
lusolver(L,U,B)
...

Answer 2

[Walter Roberson]

lumine(q)

That call executes lumine with parameter q. Then it assigns the first output to a variable named ans and displays the first output.

function [L,U] = lumine(A)

When that code is called, the variables L and U are not assigned to in the caller. L and U here are "dummy" variables, placeholders for "the first output argument" and "the second output argument". Everything in MATLAB happens positionally.

You need to assign the outputs of calling lumine, such as

[L_out, U_out] = lumine(q);

or possibly even

[L, U] = lumine(q);